IMPLICIT TIME-ACCURATE SOLUTIONS ON UNSTRUCTURED DYNAMIC GRIDS

In this paper an unstructured multigrid algorithm is used as an iterat ive solution procedure for the discrete equations arising from an impl icit time discretization of the unsteady Euler equations on tetrahedra l grids. To calculate unsteady flows due to oscillating boundaries, a novel grid movement algorithm is introduced in which an elliptic equat ion with a non-linear diffusion coefficient is used to define the disp lacement of interior grid nodes. This allows large grid displacements to be calculated in a single step. The multigrid technique uses an edg e-collapsing algorithm to generate a sequence of grids, and a pseudo-t ime-stepping smoother. On the coarser grids, no grid motion is used. I nstead, surface normals are rotated consistently and transfer/interpol ation weights are based on the time-averaged grid co-ordinates. A 2D N ACA0012 test case is used to Validate the programme. 3D results are pr esented for the M6 wing and a full aircraft configuration. (C) 1997 Jo hn Wiley & Sons, Ltd.